Abstract
In this paper we describe two pairs of raising/lowering operators for Askey- Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the "classical" properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.
| Original language | English (US) |
|---|---|
| Article number | 002 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 3 |
| DOIs | |
| State | Published - 2007 |
All Science Journal Classification (ASJC) codes
- Analysis
- Mathematical Physics
- Geometry and Topology
Keywords
- Askey-Wilson polynomials
- Double affine Hecke algebra
- Lowering operators
- Orthogonal polynomials
- Raising operators
- Root systems
- Three term recurrence
- q-difference equation